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J J M Verbaarschot - One of the best experts on this subject based on the ideXlab platform.
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spectral properties of the wilson Dirac Operator and random matrix theory
Physical Review D, 2013Co-Authors: Mario Kieburg, J J M Verbaarschot, Savvas ZafeiropoulosAbstract:Random Matrix Theory has been successfully applied to lattice Quantum Chromodynamics. In particular, a great deal of progress has been made on the understanding, numerically as well as analytically, of the spectral properties of the Wilson Dirac Operator. In this paper, we study the infra-red spectrum of the Wilson Dirac Operator via Random Matrix Theory including the three leading order $a^2$ correction terms that appear in the corresponding chiral Lagrangian. A derivation of the joint probability density of the eigenvalues is presented. This result is used to calculate the density of the complex eigenvalues, the density of the real eigenvalues and the distribution of the chiralities over the real eigenvalues. A detailed discussion of these quantities shows how each low energy constant affects the spectrum. Especially we consider the limit of small and large (which is almost the mean field limit) lattice spacing. Comparisons with Monte Carlo simulations of the Random Matrix Theory show a perfect agreement with the analytical predictions. Furthermore we present some quantities which can be easily used for comparison of lattice data and the analytical results.
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random matrix models for the hermitian wilson Dirac Operator of qcd like theories
Proceedings of The 30th International Symposium on Lattice Field Theory — PoS(Lattice 2012), 2012Co-Authors: Mario Kieburg, J J M Verbaarschot, Savvas ZafeiropoulosAbstract:We introduce Random Matrix Models for the Hermitian Wilson-Dirac Operator of QCD-like theories. We show that they are equivalent to the e-limit of the chiral Lagrangian for Wilson chiral perturbation theory. Results are obtained for two-color QCD with quarks in the fundamental representation of the color group as well as any-color QCD with quarks in the adjoint representation. For Nc = 2 we also have obtained the lattice spacing dependence of the quenched average spectral density for a fixed value of the index of the Dirac Operator. Comparisons with direct numerical simulations of the random matrix ensemble are shown.
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eigenvalue density of the non hermitian wilson Dirac Operator
Physical Review Letters, 2012Co-Authors: Mario Kieburg, J J M Verbaarschot, Savvas ZafeiropoulosAbstract:We find the lattice spacing dependence of the eigenvalue density of the non-Hermitian Wilson Dirac Operator in the ϵ domain. The starting point is the joint probability density of the corresponding random matrix theory. In addition to the density of the complex eigenvalues we also obtain the density of the real eigenvalues separately for positive and negative chiralities as well as an explicit analytical expression for the number of additional real modes.
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spectrum of the wilson Dirac Operator at finite lattice spacings
Physical Review D, 2011Co-Authors: Gernot Akemann, P H Damgaard, K Splittorff, J J M VerbaarschotAbstract:We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac Operator using both chiral perturbation theory and chiral random matrix theory. A graded chiral Lagrangian is used to evaluate the microscopic spectral density of the Hermitian Wilson Dirac Operator as well as the distribution of the chirality over the real eigenvalues of the Wilson Dirac Operator. It is shown that a chiral random matrix theory for the Wilson Dirac Operator reproduces the leading zero-momentum terms of Wilson chiral perturbation theory. All results are obtained for a fixed index of the Wilson Dirac Operator. The low-energy constants of Wilson chiral perturbation theory are shown to be constrained by the Hermiticity properties of the Wilson Dirac Operator.
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microscopic spectrum of the wilson Dirac Operator
Physical Review Letters, 2010Co-Authors: P H Damgaard, K Splittorff, J J M VerbaarschotAbstract:We calculate the leading contribution to the spectral density of the Wilson Dirac Operator using chiral perturbation theory where volume and lattice spacing corrections are given by universal scaling functions. We find analytical expressions for the spectral density on the scale of the average level spacing, and introduce a chiral random matrix theory that reproduces these results. Our work opens up a novel approach to the infinite-volume limit of lattice gauge theory at finite lattice spacing and new ways to extract coefficients of Wilson chiral perturbation theory.
P H Damgaard - One of the best experts on this subject based on the ideXlab platform.
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finite volume scaling of the wilson Dirac Operator spectrum
Physical Review D, 2012Co-Authors: P H Damgaard, U M Heller, K SplittorffAbstract:The microscopic spectral density of the Hermitian Wilson-Dirac Operator is computed numerically in quenched lattice QCD. We demonstrate that the results given for fixed index of the Wilson-Dirac Operator can be matched by the predictions from Wilson chiral perturbation theory. We test successfully the finite volume and the mass scaling predicted by Wilson chiral perturbation theory at fixed lattice spacing.
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spectrum of the wilson Dirac Operator at finite lattice spacings
Physical Review D, 2011Co-Authors: Gernot Akemann, P H Damgaard, K Splittorff, J J M VerbaarschotAbstract:We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac Operator using both chiral perturbation theory and chiral random matrix theory. A graded chiral Lagrangian is used to evaluate the microscopic spectral density of the Hermitian Wilson Dirac Operator as well as the distribution of the chirality over the real eigenvalues of the Wilson Dirac Operator. It is shown that a chiral random matrix theory for the Wilson Dirac Operator reproduces the leading zero-momentum terms of Wilson chiral perturbation theory. All results are obtained for a fixed index of the Wilson Dirac Operator. The low-energy constants of Wilson chiral perturbation theory are shown to be constrained by the Hermiticity properties of the Wilson Dirac Operator.
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microscopic spectrum of the wilson Dirac Operator
Physical Review Letters, 2010Co-Authors: P H Damgaard, K Splittorff, J J M VerbaarschotAbstract:We calculate the leading contribution to the spectral density of the Wilson Dirac Operator using chiral perturbation theory where volume and lattice spacing corrections are given by universal scaling functions. We find analytical expressions for the spectral density on the scale of the average level spacing, and introduce a chiral random matrix theory that reproduces these results. Our work opens up a novel approach to the infinite-volume limit of lattice gauge theory at finite lattice spacing and new ways to extract coefficients of Wilson chiral perturbation theory.
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the microscopic spectral density of the qcd Dirac Operator
Nuclear Physics, 1999Co-Authors: P H Damgaard, J Osborn, D Toublan, J J M VerbaarschotAbstract:Abstract We derive the microscopic spectral density of the Dirac Operator in SU ( N c ⩾ 3) Yang-Mills theory coupled to N f fermions in the fundamental representation. An essential technical ingredient is an exact rewriting of this density in terms of integrations over the super Riemannian manifold Gl (N f + 1 1 ) . The result agrees exactly with earlier calculations based on Random Matrix Theory.
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the qcd Dirac Operator spectrum and finite volume scaling
arXiv: High Energy Physics - Lattice, 1999Co-Authors: P H DamgaardAbstract:Abstract Random matrix theory and chiral Lagrangians offer a convenient tool for the exact calculation of microscopic spectral correlators of the Dirac Operator in a well-defined finite-volume scaling regime.
Savvas Zafeiropoulos - One of the best experts on this subject based on the ideXlab platform.
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spectral properties of the wilson Dirac Operator and random matrix theory
Physical Review D, 2013Co-Authors: Mario Kieburg, J J M Verbaarschot, Savvas ZafeiropoulosAbstract:Random Matrix Theory has been successfully applied to lattice Quantum Chromodynamics. In particular, a great deal of progress has been made on the understanding, numerically as well as analytically, of the spectral properties of the Wilson Dirac Operator. In this paper, we study the infra-red spectrum of the Wilson Dirac Operator via Random Matrix Theory including the three leading order $a^2$ correction terms that appear in the corresponding chiral Lagrangian. A derivation of the joint probability density of the eigenvalues is presented. This result is used to calculate the density of the complex eigenvalues, the density of the real eigenvalues and the distribution of the chiralities over the real eigenvalues. A detailed discussion of these quantities shows how each low energy constant affects the spectrum. Especially we consider the limit of small and large (which is almost the mean field limit) lattice spacing. Comparisons with Monte Carlo simulations of the Random Matrix Theory show a perfect agreement with the analytical predictions. Furthermore we present some quantities which can be easily used for comparison of lattice data and the analytical results.
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random matrix models for the hermitian wilson Dirac Operator of qcd like theories
Proceedings of The 30th International Symposium on Lattice Field Theory — PoS(Lattice 2012), 2012Co-Authors: Mario Kieburg, J J M Verbaarschot, Savvas ZafeiropoulosAbstract:We introduce Random Matrix Models for the Hermitian Wilson-Dirac Operator of QCD-like theories. We show that they are equivalent to the e-limit of the chiral Lagrangian for Wilson chiral perturbation theory. Results are obtained for two-color QCD with quarks in the fundamental representation of the color group as well as any-color QCD with quarks in the adjoint representation. For Nc = 2 we also have obtained the lattice spacing dependence of the quenched average spectral density for a fixed value of the index of the Dirac Operator. Comparisons with direct numerical simulations of the random matrix ensemble are shown.
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eigenvalue density of the non hermitian wilson Dirac Operator
Physical Review Letters, 2012Co-Authors: Mario Kieburg, J J M Verbaarschot, Savvas ZafeiropoulosAbstract:We find the lattice spacing dependence of the eigenvalue density of the non-Hermitian Wilson Dirac Operator in the ϵ domain. The starting point is the joint probability density of the corresponding random matrix theory. In addition to the density of the complex eigenvalues we also obtain the density of the real eigenvalues separately for positive and negative chiralities as well as an explicit analytical expression for the number of additional real modes.
K Splittorff - One of the best experts on this subject based on the ideXlab platform.
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finite volume scaling of the wilson Dirac Operator spectrum
Physical Review D, 2012Co-Authors: P H Damgaard, U M Heller, K SplittorffAbstract:The microscopic spectral density of the Hermitian Wilson-Dirac Operator is computed numerically in quenched lattice QCD. We demonstrate that the results given for fixed index of the Wilson-Dirac Operator can be matched by the predictions from Wilson chiral perturbation theory. We test successfully the finite volume and the mass scaling predicted by Wilson chiral perturbation theory at fixed lattice spacing.
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spectrum of the wilson Dirac Operator at finite lattice spacings
Physical Review D, 2011Co-Authors: Gernot Akemann, P H Damgaard, K Splittorff, J J M VerbaarschotAbstract:We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac Operator using both chiral perturbation theory and chiral random matrix theory. A graded chiral Lagrangian is used to evaluate the microscopic spectral density of the Hermitian Wilson Dirac Operator as well as the distribution of the chirality over the real eigenvalues of the Wilson Dirac Operator. It is shown that a chiral random matrix theory for the Wilson Dirac Operator reproduces the leading zero-momentum terms of Wilson chiral perturbation theory. All results are obtained for a fixed index of the Wilson Dirac Operator. The low-energy constants of Wilson chiral perturbation theory are shown to be constrained by the Hermiticity properties of the Wilson Dirac Operator.
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microscopic spectrum of the wilson Dirac Operator
Physical Review Letters, 2010Co-Authors: P H Damgaard, K Splittorff, J J M VerbaarschotAbstract:We calculate the leading contribution to the spectral density of the Wilson Dirac Operator using chiral perturbation theory where volume and lattice spacing corrections are given by universal scaling functions. We find analytical expressions for the spectral density on the scale of the average level spacing, and introduce a chiral random matrix theory that reproduces these results. Our work opens up a novel approach to the infinite-volume limit of lattice gauge theory at finite lattice spacing and new ways to extract coefficients of Wilson chiral perturbation theory.
Tilo Wettig - One of the best experts on this subject based on the ideXlab platform.
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qcd Dirac Operator at nonzero chemical potential lattice data and matrix model
Physical Review Letters, 2004Co-Authors: Gernot Akemann, Tilo WettigAbstract:Recently, a non-Hermitian chiral random matrix model was proposed to describe the eigenvalues of the QCD Dirac Operator at nonzero chemical potential. This matrix model can be constructed from QCD by mapping it to an equivalent matrix model which has the same symmetries as QCD with chemical potential. Its microscopic spectral correlations are conjectured to be identical to those of the QCD Dirac Operator. We investigate this conjecture by comparing large ensembles of Dirac eigenvalues in quenched SU(3) lattice QCD at a nonzero chemical potential to the analytical predictions of the matrix model. Excellent agreement is found in the two regimes of weak and strong non-Hermiticity, for several different lattice volumes.
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microscopic universality in the spectrum of the lattice Dirac Operator
Physical Review Letters, 1998Co-Authors: M E Berbennibitsch, J J M Verbaarschot, Tilo Wettig, S Meyer, A SchaferAbstract:Large ensembles of complete spectra of the Euclidean Dirac Operator for staggered fermions are calculated for SU(2) lattice gauge theory. The accumulation of eigenvalues near zero is analyzed as a signal of chiral symmetry breaking and compared with parameter-free predictions from chiral random-matrix theory. Excellent agreement for the distribution of the smallest eigenvalue and the microscopic spectral density is found. This provides direct evidence for the conjecture that these quantities are universal functions.
